
Observe that in the preceding theorem neither of the assumptions
\(\pi (\lbrace \alpha _{\bf {x}}\rbrace )=0\)  nor
\(\alpha _{\bf {x}}\in C_0(\mathcal {K})\) 
can be omitted.
For example, a hypergroup of compact type is \(\alpha \) -amenable in
every character \(\alpha \)  while
1 is the only character in \(\widehat{K}\)  with the vanishing
Plancherel measure [1]}, [2]}; see also Example (VI).

Theorem REF  is known for \(m=d=1\)  in
[3]}.



